The formulas are published in a programming language called M. There is an open source implementation [1].
> There is currently no legal guarantee of any kind about the correctness of the code produced by the Mlang compiler, or by the results produced by the interpreter of Mlang. However, authors have been in contact with DGFiP to validate Mlang, and the system passes all the private DGFiP tests as of Sept. 2022 for the version of the source files responsible for computing the tax on the 2018, 2019, 2020 and 2021 income.
MUMPS ("Massachusetts General Hospital Utility Multi-Programming System"), or M, is an imperative, high-level programming language with an integrated transaction processing key–value database. It was originally developed at Massachusetts General Hospital for managing hospital laboratory information systems.
Useful comment. Unfortunately M or MUMPS is still in active use at EPIC, etc. Far too many good grads of midwest schools get sucked into working for EPIC or the insurance mines in Des Moines, Omaha, etc. UW Madison, UIUC, and Michigan are way too good of schools to be sending their grads to work on medical records or insurance.
> There is currently no legal guarantee of any kind about the correctness of the code produced by the Mlang compiler, or by the results produced by the interpreter of Mlang. However, authors have been in contact with DGFiP to validate Mlang, and the system passes all the private DGFiP tests as of Sept. 2022 for the version of the source files responsible for computing the tax on the 2018, 2019, 2020 and 2021 income.
[1] https://github.com/MLanguage/mlang